The self-consistent gravitational self-force

I review the problem of motion for small bodies in General Relativity, with an emphasis on developing a self-consistent treatment of the gravitational self-force. An analysis of the various derivations extant in the literature leads me to formulate an asymptotic expansion in which the metric is expanded while a representative worldline is held fixed; I discuss the utility of this expansion for both exact point particles and asymptotically small bodies, contrasting it with a regular expansion in which both the metric and the worldline are expanded. Based on these preliminary analyses, I present a general method of deriving self-consistent equations of motion for arbitrarily structured (sufficiently compact) small bodies. My method utilizes two expansions: an inner expansion that keeps the size of the body fixed, and an outer expansion that lets the body shrink while holding its worldline fixed. By imposing the Lorenz gauge, I express the global solution to the Einstein equation in the outer expansion in terms of an integral over a worldtube of small radius surrounding the body. Appropriate boundary data on the tube are determined from a local-in-space expansion in a buffer region where both the inner and outer expansions are valid. This buffer-region expansion also results in an expression for the self-force in terms of irreducible pieces of the metric perturbation on the worldline. Based on the global solution, these pieces of the perturbation can be written in terms of a tail integral over the body's past history. This approach can be applied at any order to obtain a self-consistent approximation that is valid on long timescales, both near and far from the small body. I conclude by discussing possible extensions of my method and comparing it to alternative approaches.Comment: 44 pages, 4 figure

A Theoretical Investigation of the Drag of Generalized Aircraft Configurations in Supersonic Flow

It seems possible that, in supersonic flight, unconventional arrangements of wings and bodies may offer advantages in the form of drag reduction. It is the purpose of this report to consider the methods for determining the pressure drag for such unconventional configurations, and to consider a few of the possibilities for drag reduction in highly idealized aircraft. The idealized aircraft are defined by distributions of lift and volume in three-dimensional space, and Hayes' method of drag evaluation, which is well adapted to such problems, is the fundamental tool employed. Other methods of drag evaluation are considered also wherever they appear to offer amplifications. The basic singularities such as sources, dipoles, lifting elements and volume elements are discussed, and some of the useful inter-relations between these elements are presented. Hayes' method of drag evaluation is derived in detail starting with the general momentum theorem. In going from planar systems to spatial systems certain new problems arise. For example, interference between lift and thickness distributions generally appears, and such effects are used to explain the difference between the non-zero wave drag of Sears-Haack bodies and the zero wave drag of Ferrari's ring wing plus central body. Another new feature of the spatial systems is that optimum configurations generally are not unique, there being an infinite family of lift or thickness distributions producing the same minimum drag. However it is shown that all members of an optimum family produce the same flow field in a certain region external to the singularity distribution. Other results of the study indicate that certain spatial distributions may produce materially less wave drag and vortex drag than comparable planar systems. It is not at all certain that such advantages can be realized in practical aircraft designs, but further investigation seems to be warranted

Equation level matching: An extension of the method of matched asymptotic expansion for problems of wave propagation

We introduce an alternative to the method of matched asymptotic expansions. In the "traditional" implementation, approximate solutions, valid in different (but overlapping) regions are matched by using "intermediate" variables. Here we propose to match at the level of the equations involved, via a "uniform expansion" whose equations enfold those of the approximations to be matched. This has the advantage that one does not need to explicitly solve the asymptotic equations to do the matching, which can be quite impossible for some problems. In addition, it allows matching to proceed in certain wave situations where the traditional approach fails because the time behaviors differ (e.g., one of the expansions does not include dissipation). On the other hand, this approach does not provide the fairly explicit approximations resulting from standard matching. In fact, this is not even its aim, which to produce the "simplest" set of equations that capture the behavior

Gestational age at delivery and special educational need: retrospective cohort study of 407,503 schoolchildren

<STRONG>Background</STRONG> Previous studies have demonstrated an association between preterm delivery and increased risk of special educational need (SEN). The aim of our study was to examine the risk of SEN across the full range of gestation. <STRONG>Methods and Findings</STRONG> We conducted a population-based, retrospective study by linking school census data on the 407,503 eligible school-aged children resident in 19 Scottish Local Authority areas (total population 3.8 million) to their routine birth data. SEN was recorded in 17,784 (4.9%) children; 1,565 (8.4%) of those born preterm and 16,219 (4.7%) of those born at term. The risk of SEN increased across the whole range of gestation from 40 to 24 wk: 37–39 wk adjusted odds ratio (OR) 1.16, 95% confidence interval (CI) 1.12–1.20; 33–36 wk adjusted OR 1.53, 95% CI 1.43–1.63; 28–32 wk adjusted OR 2.66, 95% CI 2.38–2.97; 24–27 wk adjusted OR 6.92, 95% CI 5.58–8.58. There was no interaction between elective versus spontaneous delivery. Overall, gestation at delivery accounted for 10% of the adjusted population attributable fraction of SEN. Because of their high frequency, early term deliveries (37–39 wk) accounted for 5.5% of cases of SEN compared with preterm deliveries (<37 wk), which accounted for only 3.6% of cases. <STRONG>Conclusions</STRONG> Gestation at delivery had a strong, dose-dependent relationship with SEN that was apparent across the whole range of gestation. Because early term delivery is more common than preterm delivery, the former accounts for a higher percentage of SEN cases. Our findings have important implications for clinical practice in relation to the timing of elective delivery

Probing the role of the cation–π interaction in the binding sites of GPCRs using unnatural amino acids

We describe a general application of the nonsense suppression methodology for unnatural amino acid incorporation to probe drug–receptor interactions in functional G protein-coupled receptors (GPCRs), evaluating the binding sites of both the M2 muscarinic acetylcholine receptor and the D2 dopamine receptor. Receptors were expressed in Xenopus oocytes, and activation of a G protein-coupled, inward-rectifying K^+ channel (GIRK) provided, after optimization of conditions, a quantitative readout of receptor function. A number of aromatic amino acids thought to be near the agonist-binding site were evaluated. Incorporation of a series of fluorinated tryptophan derivatives at W6.48 of the D2 receptor establishes a cation–π interaction between the agonist dopamine and W6.48, suggesting a reorientation of W6.48 on agonist binding, consistent with proposed “rotamer switch” models. Interestingly, no comparable cation–π interaction was found at the aligning residue in the M2 receptor

Simple Viscous Flows: from Boundary Layers to the Renormalization Group

The seemingly simple problem of determining the drag on a body moving through a very viscous fluid has, for over 150 years, been a source of theoretical confusion, mathematical paradoxes, and experimental artifacts, primarily arising from the complex boundary layer structure of the flow near the body and at infinity. We review the extensive experimental and theoretical literature on this problem, with special emphasis on the logical relationship between different approaches. The survey begins with the developments of matched asymptotic expansions, and concludes with a discussion of perturbative renormalization group techniques, adapted from quantum field theory to differential equations. The renormalization group calculations lead to a new prediction for the drag coefficient, one which can both reproduce and surpass the results of matched asymptotics

Electronic sculpting of ligand-GPCR subtype selectivity:the case of angiotensin II

GPCR subtypes possess distinct functional and pharmacological profiles, and thus development of subtype-selective ligands has immense therapeutic potential. This is especially the case for the angiotensin receptor subtypes AT1R and AT2R, where a functional negative control has been described and AT2R activation highlighted as an important cancer drug target. We describe a strategy to fine-tune ligand selectivity for the AT2R/AT1R subtypes through electronic control of ligand aromatic-prolyl interactions. Through this strategy an AT2R high affinity (<i>K</i>_i = 3 nM) agonist analogue that exerted 18,000-fold higher selectivity for AT2R versus AT1R was obtained. We show that this compound is a negative regulator of AT1R signaling since it is able to inhibit MCF-7 breast carcinoma cellular proliferation in the low nanomolar range

Finite size effects near the onset of the oscillatory instability

A system of two complex Ginzburg - Landau equations is considered that applies at the onset of the oscillatory instability in spatial domains whose size is large (but finite) in one direction; the dependent variables are the slowly modulated complex amplitudes of two counterpropagating wavetrains. In order to obtain a well posed problem, four boundary conditions must be imposed at the boundaries. Two of them were already known, and the other two are first derived in this paper. In the generic case when the group velocity is of order unity, the resulting problem has terms that are not of the same order of magnitude. This fact allows us to consider two distinguished limits and to derive two associated (simpler) sub-models, that are briefly discussed. Our results predict quite a rich variety of complex dynamics that is due to both the modulational instability and finite size effects

Trade-Offs Between Morphology and Thermal Niches Mediate Adaptation in Response to Competing Selective Pressures

Abstract The effects of climate change—such as increased temperature variability and novel predators—rarely happen in isolation, but it is unclear how organisms cope with multiple stressors simultaneously. To explore this, we grew replicate Paramecium caudatum populations in either constant or variable temperatures and exposed half to predation. We then fit thermal performance curves (TPCs) of intrinsic growth rate (rmax) for each replicate population (N = 12) across seven temperatures (10°C–38°C). TPCs of P. caudatum exposed to both temperature variability and predation responded only to one or the other (but not both), resulting in unpredictable outcomes. These changes in TPCs were accompanied by changes in cell morphology. Although cell volume was conserved across treatments, cells became narrower in response to temperature variability and rounder in response to predation. Our findings suggest that predation and temperature variability produce conflicting pressures on both thermal performance and cell morphology. Lastly, we found a strong correlation between changes in cell morphology and TPC parameters in response to predation, suggesting that responses to opposing selective pressures could be constrained by trade-offs. Our results shed new light on how environmental and ecological pressures interact to elicit changes in characteristics at both the individual and population levels. We further suggest that morphological responses to interactive environmental forces may modulate population-level responses, making prediction of long-term responses to environmental change challenging